Editing S-matrix (section)

== Use ==

The ''S''-matrix is closely related to the transition [[probability amplitude]] in quantum mechanics and to [[cross section (physics)|cross sections]] of various interactions; the [[Matrix element (physics)|elements]] (individual numerical entries) in the ''S''-matrix are known as '''scattering amplitudes'''. [[pole (complex analysis)|Poles]] of the ''S''-matrix in the complex-energy plane are identified with [[bound state]]s, virtual states or [[resonance (particle physics)|resonances]]. [[Branch point|Branch cuts]] of the ''S''-matrix in the complex-energy plane are associated to the opening of a [[scattering channel]].

In the [[Hamiltonian (quantum mechanics)|Hamiltonian]] approach to quantum field theory, the ''S''-matrix may be calculated as a [[time-ordered]] [[matrix exponential|exponential]] of the integrated Hamiltonian in the [[interaction picture]]; it may also be expressed using [[Feynman's path integral]]s. In both cases, the [[perturbation theory (quantum mechanics)|perturbative]] calculation of the ''S''-matrix leads to [[Feynman diagram]]s.

In [[scattering theory]], the '''''S''-matrix''' is an [[operator (physics)|operator]] mapping free particle ''in-states'' to free particle ''out-states'' ([[scattering channel]]s) in the [[Heisenberg picture]]. This is very useful because often we cannot describe the interaction (at least, not the most interesting ones) exactly.